中文摘要：

设X是无限维Banach空间，首先证明了x中存在两个强可逼近集A，B，满足A＋B不是可逼近的；其次利用紧性证明了X中的紧集与强可逼近集的和是强可逼近的，以及X的有限维子空间与强可逼近子空间的和是强可逼近的．这推广了经典的可逼近集（相应地，可逼近子空间）的和理论．

英文摘要：

Let X be an infinite-dimensional Banach space,it＇s first showed that there exist two strongly proximinal sets A and B of X satisfying A＋B is closed hut not proximinal. By using compactness it is proved that the sum of a compact set and a strongly proximi- nal set of X is strongly proximinal, and the sum of a finite-dimensional subspace of X and a strongly proximinal subspace of X is strongly proximinal. This generalized the classical theory on the sum of the proximinal sets（respectively, proximinal subspaces）.